The generator matrix

 1  0  0  1  1  1  2  X  1  1 X^2+X  1  1 X^2+X  1  1 X+2 X^2+X+2  1  1 X^2+X+2  1  1  1  0  1  X X+2  2 X^2+X+2  1 X^2+2  1  1  1
 0  1  0  X  3 X+1  1  1 X+2  X  1 X^2+X+3 X^2+3  2 X^2 X^2+X+3  X  1 X^2+1 X^2  1  2 X+1 X^2+2  1 X+1  2  1  1 X^2+X+2  1  1 X^2+3  0  2
 0  0  1  1  1  0 X+1 X+2  2 X^2+X+1 X+1  X X^2+X+3  1 X^2+X+2 X^2+3  1 X^2+2 X+2 X+1  1  3 X^2+X+2  2 X^2+1 X^2+X+3  1 X+1 X^2+X  1 X^2+X+3 X^2+1 X^2+X+3 X+2  0
 0  0  0 X^2 X^2+2  2 X^2  2  0  2  0 X^2+2 X^2+2  0 X^2  2 X^2+2 X^2+2 X^2  2  2  2  0 X^2+2 X^2 X^2 X^2+2 X^2+2  2 X^2 X^2  2  0 X^2+2 X^2

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+92x^30+560x^31+1281x^32+2102x^33+2544x^34+3234x^35+2788x^36+1980x^37+1068x^38+494x^39+130x^40+62x^41+24x^42+14x^43+8x^44+2x^47

The gray image is a code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 1.19 seconds.